Question

5. In AABC, if 2A + 2B = 125 and 2A + 2C = 113°, find 2A, 2B and 20.​

Answer 1

>>In ABC , if A + B = 125^∘ and A +

In △ABC, if ∠A+∠B=125

∘

and ∠A+∠C=113

∘

, find ∠A,∠B and ∠C.

It is given that ∠A+∠B=125

∘

…(1)

We know that the sum of all the angles in a triangle is 180

∘

.

So we can write it as

∠A+∠B+∠C=180

∘

By substituting ∠A+∠B=125

∘

in the above equation

125

∘

+∠C=180

∘

On further calculation

∠C=180

∘

−125

∘

By subtraction

∠C=55

∘

It is given that ∠A+∠C=113

∘

By substituting the value of ∠C

∠A+55

∘

=113

∘

On further calculation

∠A=113

∘

−55

∘

By subtraction

∠A=58

∘

By substituting ∠A=58

∘

in equation (1)

So we get

∠A+∠B=125

∘

58

∘

+∠B=125

∘

On further calculation

∠B=125

∘

−58

∘

By subtraction

∠B=67

∘

Therefore, ∠A=58

∘

,∠B=67

∘

and ∠C=55

∘

.

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